{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Determine the number of bits to flip to convert int a to int b.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume A and B are always ints?\n",
    "    * Yes\n",
    "* Is the output an int?\n",
    "    * Yes\n",
    "* Can we assume A and B are always the same number of bits?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid (not None)?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* A or B is None -> Exception\n",
    "* General case\n",
    "<pre>\n",
    "    A = 11101\n",
    "    B = 01111\n",
    "    Result: 2\n",
    "<pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We can use the xor operator to determine the bit differences between a and b\n",
    "\n",
    "* Set count to 0\n",
    "* Set c to a xor b\n",
    "* Loop while c != 0:\n",
    "    * Increment count if the LSB in c is a 1\n",
    "        * We can check this by using a mask of 1\n",
    "    * Right shift c by 1\n",
    "* Return the count\n",
    "    \n",
    "Complexity:\n",
    "* Time: O(b), where b is the number of bits\n",
    "* Space: O(b), where b is the number of bits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Bits(object):\n",
    "\n",
    "    def bits_to_flip(self, a, b):\n",
    "        if a is None or b is None:\n",
    "            raise TypeError('a or b cannot be None')\n",
    "        count = 0\n",
    "        c = a ^ b\n",
    "        while c:\n",
    "            count += c & 1\n",
    "            c >>= 1\n",
    "        return count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_bits_to_flip.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_bits_to_flip.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestBits(unittest.TestCase):\n",
    "\n",
    "    def test_bits_to_flip(self):\n",
    "        bits = Bits()\n",
    "        a = int('11101', base=2)\n",
    "        b = int('01111', base=2)\n",
    "        expected = 2\n",
    "        self.assertEqual(bits.bits_to_flip(a, b), expected)\n",
    "        print('Success: test_bits_to_flip')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestBits()\n",
    "    test.test_bits_to_flip()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_bits_to_flip\n"
     ]
    }
   ],
   "source": [
    "%run -i test_bits_to_flip.py"
   ]
  }
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